There are 6 orange sweets and n sweets overall. So, if Hannah takes one, there is 6/n chance of getting an orange sweet. When she takes one,, there is one less orange sweet and one less overall meaning that the probability is now (6-1)/(n-1)=5/n-1.

To find the probability of getting the orange sweet both times, multiply the two fractions: 6/n* 5/n-1 =30/n^2-n.

It shows the probability of taking two orange sweets (1/3) is: 1/3=30/n^2-n.

The denominators then need to be the same, so multiply 1/3 by 30 which would then make 30/90=30/n^2-n.

Discounting the 30 on both sides of the equation makes n^2-n=90. By moving 90 onto the other side of the equation, it will equal zero.